In the art of measuring mass flow rates of flowing substances it is known that flowing a fluid through a rotating or oscillating conduit produces Coriolis forces which are perpendicular to both the velocity of the mass moving through the conduit and the angular velocity vector of the rotation or oscillation of the conduit. It is also known that the magnitude of such Coriolis forces is related to the mass flow rate as a function of the angular velocity of the conduit.
One of the major technical problems previously associated with Coriolis mass flow rate instruments was the accurate measurement of Coriolis force effects such as conduit deflection. This problem arises in part because the magnitude of the Coriolis forces for moderate mass flow rates and reasonable angular velocities may be very small, resulting in small conduit deflections or other effects, which necessitates the use of sensitive and accurate instrumentation. Furthermore, in order to determine the mass flow rate passing through the conduit as a function of the magnitude of the generated Coriolis forces, the magnitude of the angular velocity of the conduit must also be either accurately measured or precisely controlled.
A mechanical configuration and measurement technique which, among other advantages, avoid the need to measure or control the magnitude of the angular velocity of the conduit, and concurrently provide requisite sensitivity and accuracy of measurement of the effects caused by generated Coriolis forces is taught in U.S. Pat. No. Re. 31,450. The mechanical configuration disclosed in that patent incorporates a resilient U-shaped flow tube which has no pressure sensitive joints, and is cantilever mounted at the open ends of the U-shaped flow tube so as to be capable of being elastically oscillated about an axis perpendicular to the side legs of the U-shaped flow tube, which axis is located near the fixed mounting and in the plane in which the U-shaped flow tube lies when at rest; i.e., the midplane of oscillation. When a substance is flowing through the U-shaped flow tube, and that tube is thus mounted, oscillation of the filled U-shaped flow tube so that its free end passes through the mid-plane of oscillation, causes the generation of a Coriolis force couple which can elastically deflect the free end of the U-shaped flow tube about an axis located in the plane of the U-shaped flow tube midway between and parallel to the side legs of the U-shaped flow tube. By designing the mounted U-shaped flow tube so that it has a resonant frequency about the axis perpendicular to the side legs of the U-shaped flow tube that is lower than the resonant frequency about the axis parallel to the side legs of the U-shaped flow tube and by then oscillating the U-shaped flow tube about the axis perpendicular to the side legs of the U-shaped flow tube at its resonant frequency, a mechanical situation is created whereby the forces which oppose the generated Coriolis forces are predominantly linear spring forces. This fact, that the forces opposing the generated Coriolis forces are predominantly linear spring forces, causes one side leg of the U-shaped flow tube to pass through the mid-plane of oscillation before the other side leg does so, in a linear fashion. Occurrence of these events results in a situation where measurement of the time interval between the passage of the respective side legs through the mid-plane of oscillation provides a direct means, without regard to the angular velocity of the U-shaped flow tube or other variable terms, for calculating the mass flow rate of the fluid passing through the U-shaped flow tube. Such time difference measurements can accurately be made by using optical sensors as disclosed in U.S. Pat. No. Re. 31,450, or by using electromagnetic velocity sensors as disclosed in U.S. Pat. No. 4,422,338.
Also included as part of the mechanical configuration for the Coriolis mass flow rate instruments as taught in U.S. Pat. No. Re. 31,450 is cantilever mounting of a second structure in conjunction with the U-shaped flow tube. This second structure is so mounted and designed that when it is sinusoidally driven in opposition to the U-shaped flow tube the combination of the second structure and the U-shaped flow tube operate as a tuning fork. Among the advantages achieved by tuning fork operation is substantial attenuation, at the support, of vibration forces associated with the sinusoidal driving of the U-shaped flow tube and the second structure. This attenuation of vibration forces at the support from which the U-shaped flow tube and the second structure are cantilever mounted is not only a desirable consequence because of the long term fatigue effects vibration forces could have on the mounting structure of the meter, but also is a very important consequence because of the errors such vibration forces could introduce into the time interval measurements of the passage of the respective side legs through the mid-plane of oscillation. The error referred to here is critical, because the accuracy with which the time interval measurements are made is directly proportional to the determination of mass flow rate. Effects of vibrations which could produce errors in the time interval measurements include vibration induced displacement of structures on which sensors are mounted to indicate passage of the respective side legs of the U-shaped flow tube through the mid-plane of oscillation. Displacement of such structures with respect to the mid-plane of oscillation, accordingly, render signals from the sensors inaccurate.
As taught in U.S. Pat. No. Re. 31,450 the cantilever mounted second structure is a spring arm. Substituting for the spring arm a second flow tube similarly configured to the first flow tube, an expedient within the ordinary skill of the art, provides an inherently balanced tuning fork structure because of the symmetries incorporated in the operation of the tines. Recognition of this fact has been used in the design of densimeters where measurements of the resonance frequency of cantilever mounted filled flow tubes are made to determine the density of fluids in the tubes, see, e.g., U.S. Pat. No. 2,635,462 and 3,456,491.
The double flow tube configuration has also been used for making mass flow rate measurements, see, e.g., U.S. Pat. Nos. 4,127,028; 4,192,184; and 4,311,054. These double flow tube meters utilize a fluid flow path wherein the fluid enters one leg of one of the flow tubes, through which it is passed, and then is transported via an interconnecting conduit to the second flow tube, through which it is passed, before exiting from the meter. Such a fluid flow path through the two flow tubes can be accurately described as a serial flow path configuration.
Inherently associated with series type double flow tube meters is a doubling of the fluid pressure drop across the meter. This results from the fact that all the fluid has to pass through two flow tubes as opposed to one. Such fluid pressure drops are a detrimental feature associated with monitoring fluid flow because as the pressure drop increases, compensating augmentation of fluid pumping is required to offset losses in the fluid pressure delivered from the conduit system incorporating series type double flow tube meters.